Place chicken in a single layer in a large pot and cover with water. Bring to a boil, cover, reduce heat and simmer until cooked, about 7 minutes. Drain, transfer chicken onto a bowl or plate, let cool and shred.
In a large, deep skillet, heat 1 cup oil until it reaches 360 degrees Fahrenheit (use a candy thermometer). Fry 1 tortilla for about 1 minute or until crisp, flipping the tortilla halfway through. Remove tortilla onto a plate. Let oil return to 360 degrees and repeat.
Warm the remaining 1 tablespoons oil in a separate skillet over medium heat. Add onion and bell pepper, salt and pepper, and cook 7 minutes. Stir in adobo sauce and chicken, and saute for 2 minutes. Top the tortillas with the chicken mixture, lettuce and tomato, cheddar cheese and sour cream.